Question: Simplify the following expression: $a = \dfrac{-4k^2 - 60k - 216}{k + 9} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ a =\dfrac{-4(k^2 + 15k + 54)}{k + 9} $ Then we factor the remaining polynomial: $k^2 + {15}k + {54} $ ${9} + {6} = {15}$ ${9} \times {6} = {54}$ $ (k + {9}) (k + {6}) $ This gives us a factored expression: $\dfrac{-4(k + {9}) (k + {6})}{k + 9}$ We can divide the numerator and denominator by $(k - 9)$ on condition that $k \neq -9$ Therefore $a = -4(k + 6); k \neq -9$